Convexity Adjustments for ATS Models

Abstract

We present a general technique to obtain closed form convexity adjustments in an affine term structure set up, for products that are non-standard in terms of the timing or the rate of payment. We show how convexity adjustments are related to affine functionals, and as particular examples, we concentrate on the LIBOR in arrears and constant maturity swaps. Specifically, we contrast the convexity adjustments computed for Vasicek and CIR models, and show that the models produce convexity adjustments of different size and shape across the term structure. We also study in detail the impact of the mean reversion parameter and volatility on the shape and size of the convexity adjustment.

Keywords: affine term structure, convexity adjustments, CMS, LIBOR in arrears

JEL Classification: C02, C65, E43, G12